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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 182070.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 182070.h1 | 182070ed4 | \([1, -1, 0, -14650620, -12979301104]\) | \(731992986690867/270340772800\) | \(128438839148405920545600\) | \([2]\) | \(19906560\) | \(3.1342\) | |
| 182070.h2 | 182070ed2 | \([1, -1, 0, -6305745, 6095515321]\) | \(42547659109328043/6195437500\) | \(4037655603818812500\) | \([2]\) | \(6635520\) | \(2.5849\) | |
| 182070.h3 | 182070ed1 | \([1, -1, 0, -358125, 113399125]\) | \(-7794190562283/4000066000\) | \(-2606900465147958000\) | \([2]\) | \(3317760\) | \(2.2383\) | \(\Gamma_0(N)\)-optimal |
| 182070.h4 | 182070ed3 | \([1, -1, 0, 2828100, -1439850160]\) | \(5265299629773/4930293760\) | \(-2342381434499729387520\) | \([2]\) | \(9953280\) | \(2.7877\) |
Rank
sage: E.rank()
The elliptic curves in class 182070.h have rank \(1\).
Complex multiplication
The elliptic curves in class 182070.h do not have complex multiplication.Modular form 182070.2.a.h
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
